# How to rule out that the speed of light was different in the past?

• I
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α is absolutely not the speed of light morphed into a dimensionless form.
Insofar as it is anything at all besides α, it is the charge of the electron morphed into a dimensionless form.

c is a factor that comes about because we historically measured time in seconds and length in meters. (And is equal to a dimensionless 1 in sane units). It's a conversion factor, like the dozen. No more, no less. It tells us about spacetime, not electromagnetism.
No, the charge of the electron is defined to be ##-e## in the SI. As detailed in #27 the ingredient of ##\alpha## that's not defined since 2019 by defining the units s, m, kg, and A, is the "permittivity of the vacuum", ##\epsilon_0## which is now to be measured. The same holds for the "permeability of the vacuum", ##\mu_0##, which now is no longer defined but has to be measured. In the SI before 2019 (since 1948 or so) ##\mu_0## was defined through the definition of the A via the force of two infinitelylong straight wires of negligible width: ##\mu_0^{(\text{old})}=4 \pi \cdot 10^{-7} \text{N} \cdot \text{A}^{-2}##. Now it's to be measured and the current value is ##μ_0^{(\text{new})} = 1.25663706212(19) \cdot 10^{-6} \text{N}\cdot \text{A}^{-2}##.

Staff Emeritus
To be fair, his question is basically "How can we be so sure it hasn't changed if we can't measure it?"
Then I would argue that if you can't tell, you're free to use any units you want.

Yes, but then do the permittivity and permeability ratio of vacuum (free space) could be different some billions of years ago?
I think there is a redundancy between the three "constants of nature" in
##c= \frac{1}{\sqrt{\epsilon_0 \mu_0}}##. Only two of them are needed. The third is only calculated from the other two and could be substituted in all physics books. I would regard ##\mu_0## as least important, because the magnetic field is only a Lorentz-transformed electric field and there exist no magnetic monopoles.

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It's a matter of definition, and within the SI ##c## is defined, and both ##\epsilon_0## and ##\mu_0## must be measured somehow. It's of course enough to measure one of them and then use the relation to ##c## to calculate the other.

Historically it was the other way around: the analogue of ##\epsilon_0## and ##\mu_0## was known in the 19th century from measuring the relation of the charge in electrostatic and magnetostatic units (Kohlrausch and Weber 1855, measuring the charge on a Leiden bottle by measuring forces on test charges (electrostatic measurement) and comparing it to the magnetic flux due to the current when discharging it (magnetostatic measurement)).

Then famously Maxwell discovered his equations of the electromagnetic field, i.e., he added the "displacement current" to the Ampere Law, as it was known from action-at-a-distance models (e.g., a la Neumann) at the time, and predicted the existence of electromagnetic waves with a phase velocity given by the said relation between electrostatic and magnetostatic units of charge, which is analogous to ##c=1/\sqrt{\epsilon_0 \mu_0}## when using SI units. The resulting value was pretty close to the then known speed of light, so that Maxwell could conjecture that light might be just electromagnetic waves.

Sagittarius A-Star
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How do we know that a dozen was twelve in the past?
Its not translation-invariant, some locations around me it is 13 or 14, depending on whether bagels or donuts are involved

vanhees71 and hutchphd
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I think it makes it worse and not better. It mixes the fundamental with the practical.

Then I would argue that if you can't tell, you're free to use any units you want.
That was my point

Staff Emeritus
permeability ratio of vacuum
Is an artifact of our system of units. (This was clearer under the older definitions) Did you think it was a measured quantity and just happened to be 4π? Gosh, what are the chances of that!

The c that comes here is the same c in the Lorentz force law (and is 1 for suitable choice of velocity units).

Maybe the way to think about it is this way. Back when solving trig identities, the teacher said that $\sin^2 \phi + \cos^2 \phi$ is "just a fancy way of writing 1". In exactly the same way, 300,000 m/s is "just a fancy way of writing 1". Asking whether it was different in the past is the same as asking if the number 1 was different in the past.

Just as 1 meter to the left is the same as 1 meter up, 300,000 meters is the same as 1 second.

Lluis Olle
Asking whether it was different in the past is the same as asking if the number 1 was different in the past.
I think that observations from distant Galaxies (which is kind of looking into the past), don't rule out that c was different (compared to our local and current environment).

Motore and PeroK
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I think that observations from distant Galaxies (which is kind of looking into the past), don't rule out that c was different (compared to our local and current environment).
Why do you think that?

Lluis Olle
Why do you think that?
Because is my understanding that the concept of the "uniformity" of c is a local concept, and could be not so "uniform" at the cosmological level. And for "local" I mean in the spacetime sense.

weirdoguy and PeroK
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Because is my understanding that the concept of the "uniformity" of c is a local concept, and could be not so "uniform" at the cosmological level. And for "local" I mean in the spacetime sense.
It makes no sense to say that the local ##c## here is different from the local ##c## there. This, again, is where you need a change that affects the observed physical phenomena - like the spectrum of hydrogen.

Lluis Olle and vanhees71
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my understanding that the concept of the "uniformity" of c is a local concept

Perhaps you are conflating locally flat spacetime with what you call uniformity of c.

Lluis Olle
It makes no sense to say that the local ##c## here is different from the local ##c## there. This, again, is where you need a change that affects the observed physical phenomena - like the spectrum of hydrogen.
As I said, "here" and "there" are spacetime concepts at the cosmological level in the context I'm talking. If I'm not wrong (that would be no surprise for me anyway), even Einstein considered that GR was "locally" correct, but...

And there's an open debate about the "redshift" of Quasars...

Lluis Olle
Perhaps you are conflating locally flat spacetime with what you call uniformity of c.
Outside the "locality" environment - which I'm unable to say if it's 1 billion YL or whatever -, who knows? It's not obvious, and the scientific data about Quasars and Galaxies is an open debate.

Mentor
So, assuming that other dimensionful constants involved in this particular ratio known as α were not different in the past, say in 2 billion years ago, we can refer to the data from the Oklo mine natural nuclear reactor. And it looks like we have experimental evidence here on our planet from at least 2 billion years ago, ruling out that the speed of light was different in the past!
Yes. However, if you are assuming that ##c## could vary then it is a little odd to assume that none of the other constants in ##\alpha## can vary. To me, that assumption is objectionable.

Since we are detecting a possible variation in ##\alpha## it is far better (in my opinion) to simply measure it and report any variation than to try to assert that such variation in ##\alpha## corresponds to a variation in ##c##.

victorvmotti
Since we are detecting a possible variation in ##\alpha## it is far better (in my opinion) to simply measure it and report any variation than to try to assert that such variation in ##\alpha## corresponds to a variation in ##c##.

So back again to your point earlier. It is impossible, logically, to know if the speed of light was different in the past or not!

Mentor
So back again to your point earlier. It is impossible, logically, to know if the speed of light was different in the past or not!
Right. We can experimentally test for variations in ##\alpha##, and all of the physics are captured by that. Anything further that we try to say specifically about ##c## is just an assumption.

Since $$\alpha=\frac{e^2}{2 \epsilon_0 h c}$$ we can take a non-variation in ##\alpha## to mean that ##c## has doubled and ##h## has halved!

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To me, that assumption is objectionable.
Well of course big claims demand axtraordinary evidence. But the Hubble redshift assertions do make a tempting target!

Staff Emeritus
little odd to assume that none of the other constants in can vary.
Especially because c is present in the definition of the fine structure constant in some systems of units and not others.

In MKSA, $\alpha = e^2/2\epsilon_0 hc$. If it varies, my money is on the 2 changing. After all, LEP at CERN measured the number 3 experimentally and got 2.99 +/- 0.01.

hutchphd and Dale
Einstein considered that GR was "locally" correct, but...
Do you have a related link?

And there's an open debate about the "redshift" of Quasars...
If you refer to the "tired light" hypothesis, there exists evidence against it, for example
The tired light model does not predict the observed time dilation of high redshift supernova light curves. This time dilation is a consequence of the standard interpretation of the redshift: a supernova that takes 20 days to decay will appear to take 40 days to decay when observed at redshift z=1.
Source:
https://astro.ucla.edu/~wright/tiredlit.htm

PeroK
Mentor
is my understanding that the concept of the "uniformity" of c is a local concept
Where are you getting that understanding from? Please give a reference.

Lluis Olle
Mentor
there's an open debate about the "redshift" of Quasars...
What open debate? Please give a reference.

PeroK
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Right. We can experimentally test for variations in ##\alpha##, and all of the physics are captured by that. Anything further that we try to say specifically about ##c## is just an assumption.

Since $$\alpha=\frac{e^2}{2 \epsilon_0 h c}$$ we can take a non-variation in ##\alpha## to mean that ##c## has doubled and ##h## has halved!
No! Since 2019 we can't do this, because ##c##, ##h##, and ##e## are fixed within the SI to define the units used to do measurements. What's not defined but must be measured is now ##\epsilon_0##! So using the new SI it's ##\epsilon_0## that may have changed with time. So far there's no hint at such a variation modulo the (high) accuracy in measuring spectral lines from far-distant objects.

Mentor
No! Since 2019 we can't do this, because c, h, and e are fixed within the SI to define the units used to do measurements.
Sure we could. We could just use non-SI units.

Motore, hutchphd and vanhees71
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E.g., we can just use the old SI. There we had ##\Delta \nu_{\text{CS}}## and ##c## as in the new SI, but the kg was still defined by the prototype in Paris, and the A was defined via setting ##\mu_0=4 \pi \cdot 10^{-7} \text{N} \cdot \text{A}^{-2}##. Thus also ##\epsilon_0=1/(\mu_0 c^2)## was defined. So using the old SI units a measured change of ##\alpha## would imply a change of ##h## or ##e## (or both).

Dale
Staff Emeritus
So using the old SI units a measured change of would imply a change of ħ orc (or both).
Or π! (Of course, under the new definitions, π is a measured quantity.)

apostolosdt and vanhees71
Staff Emeritus
Let’s say that we measured a change in α, would defining the fundamental constants still be the preferred method to define units?
Let's say that we defined the kilogram by an artifact, and noticed the mass of this artifact were changing over time. Would that be a good reason to redefine units?

Oh wait...that actually happened.

apostolosdt and vanhees71
Lluis Olle
Where are you getting that understanding from? Please give a reference.
For example, in this Wikipedia article (I'm not about VSL theories!) you can read:
Accepted classical theories of physics, and in particular general relativity, predict a constant speed of light in any local frame of reference and in some situations these predict apparent variations of the speed of light depending on frame of reference, but this article does not refer to this as a variable speed of light.
You can only define and measure the "speed of light in vacuum" locally. Let's say that I measure locally the speed of light to be 299 792 458 m/s, or that I fix that value and the way I measure that value locally. If I measure then the speed of a photon that comes from a distant Galaxy or Quasar, then locally I would measure that speed... but I can't tell what was the "local" speed then and there where the photon was produced.

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Dale
Let's say that I measure locally the speed of light to be 299 792 458 m/s
That's no measurement of the speed of light. That's a measurement, if the scale on your ruler is accurate.

Mentor
You can only define and measure the "speed of light in vacuum" locally.
No, you can only directly measure the fine structure constant and things that might depend on it (like the speed of light in vacuum locally, if you are using units where that is a measured quantity instead of a defined one--note that in SI units it s defined, not measured). But that in no way means you cannot indirectly measure the fine structure constant and things that might depend on it at distant locations or in the past.

Mentor
in this Wikipedia article (I'm not about VSL theories!) you can read:

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No, you can only directly measure the fine structure constant and things that might depend on it (like the speed of light in vacuum locally, if you are using units where that is a measured quantity instead of a defined one--note that in SI units it s defined, not measured). But that in no way means you cannot indirectly measure the fine structure constant and things that might depend on it at distant locations or in the past.
Of course for each of the definition you need also the "mises en pratique" for the units. E.g., to realize the definition of the kg via the defined values Planck action ##h## (and also of the definitions of the s, the, m, and the A) with the Kibble balance what's accurately measured are quantities like the magnetic-flux quantum in superconductors (Josephson constant).

You find the corresponding brochures in English here:

https://www.bipm.org/en/publications/mises-en-pratique

Lluis Olle
No, you can only directly measure the fine structure constant and things that might depend on it (like the speed of light in vacuum locally, if you are using units where that is a measured quantity instead of a defined one--note that in SI units it s defined, not measured). But that in no way means you cannot indirectly measure the fine structure constant and things that might depend on it at distant locations or in the past.
But in the fine structure, there're other "constants" playing other than π and c.

For example, the Universe is expanding and seems the expansion is accelerating. Locally, lets say at every eventpoint of the worldline of a photon that comes from a distant Galaxy, its locally measured speed is c. But as space is expanding, then for a non-local observer the speed exceeds c if computed globally, but not measured locally.

What I don't understand (among other billion of things) is that my measuring 1 meter rod is not expanding itself, is the space outside the rod that's expanding - or I could not measure the expansion!

PeroK